Multipartite Markov Gaps and Entanglement Wedge Multiway Cuts

TL;DR

This paper introduces a multipartite generalization of the Markov gap using reflected multi-entropy, providing new insights into quantum recoverability, entanglement structure, and geometric obstructions in holographic systems.

Contribution

It proposes a novel multipartite Markov gap based on reflected multi-entropy, linking information-theoretic measures with holographic geometric interpretations.

Findings

Multipartite Markov gap captures geometric obstructions to bulk reconstruction.

Genuine reflected multi-entropy vanishes for states with only lower-partite entanglement.

The quantities serve as probes for recoverability and multipartite entanglement in holographic systems.

Abstract

The Markov gap, defined as the difference between reflected entropy and mutual information, serves as a diagnostic for quantum recoverability and multipartite entanglement. In holographic settings, it admits a geometric interpretation as the deviation between entanglement wedge cross-sections and RT surfaces. Motivated by this holographic perspective, we propose a generalization of the Markov gap to multipartite systems by using a reflected multi-entropy. The resulting Multipartite Markov gap can capture geometric obstructions to bulk reconstruction. We investigate the properties of this quantity from both information-theoretic and holographic viewpoints, and examine its potential operational significance through candidate recovery maps. We further introduce the genuine reflected multi-entropy, which is designed to vanish for states containing only lower-partite entanglement. Together, these quantities offer complementary probes of recoverability and multipartite structure in holographic quantum systems.